Contouring Structural Data: Overlapping Circle Method

The red dots show the locations of people in a village. How can we
characterize the population density from place to place?

Strictly
speaking, the population density is very high where a person is and zero
everywhere else. But we define density in terms of some area that gives
useful information, say, per one percent of the town's area.

One way to do it is to center a circle on every person. If the
circle has unit area, then everywhere within a circle centered on a
person, we have one person per unit area. Where two circles overlap,
there are two people per unit area in the overlap area.

In the example
here, for one block, density is highest in the center of the block where
we are a short distance from a lot of people.

When contouring structural data, we must use the equal area net. If
we used a stereonet, a circle of a given size would cover less angular
area near the primitive circle than it would in the center of the net.

We customarily contour in terms of points per one percent area of the
net. One percent conveniently translates into a circle with one tenth
the diameter of the net.

Some purists have been concerned about the effects of linear
distortion near the primitive circle and have gone so far as to create
ellipse templates to use for contouring different areas of the net. In
practice, there does not seem to be any significant improvement from
going that extra step.

We center a circle on each point and color code the densities.
Circles that extend beyond the primitive circle must re-enter on the
opposite side of the net (as around azimuths 060 and 240).

A simple
rule can be used for coloring. Every time you cross a circle, the
density increases by one. Start with the lowest densities and work
inward.

Advantages

Completely impartial. Barring errors, everyone who uses this
method gets the same result.

Best when data are comparatively sparse

Disadvantages

Can be hard to do accurately when data densities are very high

When data are sparse, can create a misleading impression of precision.

Computer Contouring

The easiest way to contour data by computer is a variation on this method.
Create a data array corresponding to a grid of points covering the net. For each
grid point, determine how many data points lie within a certain angular distance
and put that value in the array, then print out or display the result.